Code
#|eval: FALSE
pacman::p_load(sf,spatstat,raster,maptools,tmap)Hands-on Exercise 3: 1st Order Spatial Point Pattern Analysis Methods
1 Spatial Point Pattern Analysis
1.1 Overview
Spatial Point Pattern Analysis is the evaluation of the pattern or distribution of a set of points on a surface. The point can be location of:
events such as crime, traffic accident and disease onset,
or business services (coffee and fast food outlets) or facilities such as childcare and eldercare.
In this exercise, we will use appropriate functions of spatstat to discover the spatial point processes of childcare centres in Singapore.
The specific questions we would like to answer are as follows:
Are childcare centres in Singapore randomly distributed throughout the country?
If the answer is no, then the next logical question is: Where are the locations with higher concentration of childcare centres?
1.2 Data Acquisition
To address the above questions, we would be using the following three data sets
CHILDCARE (geojson format)
A point feature data providing both location and attribute information of childcare centres
Source: Data.gov.sg
MP14_SUBZONE_WEB_PL (ESRI shapefile format)
A polygon feature data providing information of URA 2014 Master Plan Planning Subzone boundary data
Source: Data.gov.sg
CostalOutline (ESRI shapefile format)
A polygon feature data showing the national boundary of Singapore
Source: SLA
1.3 Installing and Loading the R packages
In this exercise, the following five R packages will be used”
sf
spatspat
raster
maptools
tmap
To install and load the packages, we apply the following code:
1.4 Spatial Data Wrangling
1.4.1. Importing the spatial data
In this section, we will use st_read() from the sf package to import the three geospatial data sets into R.
Code
#|eval: FALSE
childcare_sf <- st_read(dsn = "data/ChildCareServices.geojson") %>%
st_transform(crs=3414)Reading layer `ChildCareServices' from data source
`/Users/binhui-ong/IS415-GAA/Hands-on_Ex/Hands-on_Ex03/data/ChildCareServices.geojson'
using driver `GeoJSON'
Simple feature collection with 1925 features and 2 fields
Geometry type: POINT
Dimension: XYZ
Bounding box: xmin: 103.6878 ymin: 1.247759 xmax: 103.9897 ymax: 1.462134
z_range: zmin: 0 zmax: 0
Geodetic CRS: WGS 84Code
#|eval: FALSE
sg_sf <- st_read(dsn="data", layer = "MP14_SUBZONE_WEB_PL") %>% st_union()Reading layer `MP14_SUBZONE_WEB_PL' from data source
`/Users/binhui-ong/IS415-GAA/Hands-on_Ex/Hands-on_Ex03/data'
using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21Code
#|eval: FALSE
mpsz_sf <- st_read(dsn="data", layer = "MP14_SUBZONE_WEB_PL")Reading layer `MP14_SUBZONE_WEB_PL' from data source
`/Users/binhui-ong/IS415-GAA/Hands-on_Ex/Hands-on_Ex03/data'
using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21Before we use the data sets for analysis, we should check if they have all been correctly projected into the SVY21 coordinate system,
Code
st_crs(childcare_sf)Coordinate Reference System:
User input: EPSG:3414
wkt:
PROJCRS["SVY21 / Singapore TM",
BASEGEOGCRS["SVY21",
DATUM["SVY21",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4757]],
CONVERSION["Singapore Transverse Mercator",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["northing (N)",north,
ORDER[1],
LENGTHUNIT["metre",1]],
AXIS["easting (E)",east,
ORDER[2],
LENGTHUNIT["metre",1]],
USAGE[
SCOPE["Cadastre, engineering survey, topographic mapping."],
AREA["Singapore - onshore and offshore."],
BBOX[1.13,103.59,1.47,104.07]],
ID["EPSG",3414]]Code
st_crs(sg_sf)Coordinate Reference System:
User input: SVY21
wkt:
PROJCRS["SVY21",
BASEGEOGCRS["SVY21[WGS84]",
DATUM["World Geodetic System 1984",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]],
ID["EPSG",6326]],
PRIMEM["Greenwich",0,
ANGLEUNIT["Degree",0.0174532925199433]]],
CONVERSION["unnamed",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["(E)",east,
ORDER[1],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]],
AXIS["(N)",north,
ORDER[2],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]]]Code
st_crs(mpsz_sf)Coordinate Reference System:
User input: SVY21
wkt:
PROJCRS["SVY21",
BASEGEOGCRS["SVY21[WGS84]",
DATUM["World Geodetic System 1984",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]],
ID["EPSG",6326]],
PRIMEM["Greenwich",0,
ANGLEUNIT["Degree",0.0174532925199433]]],
CONVERSION["unnamed",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["(E)",east,
ORDER[1],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]],
AXIS["(N)",north,
ORDER[2],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]]]Since the sg_sf and mpsz_sf data sets do not have the correct EPSG code, we can change them using st_set_crs().
Code
sg_sf<- st_set_crs(sg_sf, 3414)Code
mpsz_sf <- st_set_crs(mpsz_sf, 3414)1.4.2 Mapping the geospatial data sets
After checking the referencing system of each geospatial data frame, it is also useful for us to plot a map to show their spatial patterns.
Code
tm_shape(sg_sf) + tm_polygons() +
tm_shape(mpsz_sf) + tm_polygons() +
tm_shape(childcare_sf) + tm_dots()
Notice that all the geospatial layers are within the same map extend. This shows that their referencing system and coordinate values are referred to similar spatial context. This is very important in any geospatial analysis.
We can create a pin map by using the following code chunk:
Code
tmap_mode('view')
tm_shape(childcare_sf) +
tm_dots()In the interactive mode, tmap is using leaflet for R API. This interactive pin map allows us to navigate and zoom around the map freely.
Additionally, we can query the information of each simple feature (i.e. the point) by clicking it.
Lastly, we can change the background of the internet map layer. Currently, three internet map layers are provided. They are: ESRI.WorldGrayCanvas, OpenStreetMap, and ESRI.WorldTopoMap. The default is ESRI.WorldGrayCanvas.
Thereafter, we switch back to plot mode as the interactive mode will consume a connection.
Code
tmap_mode('plot')1.5 Geospatial Data Wrangling
Though simple feature data frame is gaining popularity again, many geospatial analysis packages require the input geospatial data to be in sp’s Spatial* class.
In this section, we will convert simple feature data frame to sp’s Spatial* class.
1.5.1 Converting sf data frames to sp’s Spatial* class
To convert geospatial data from sf data frame to sp’s Spatial* class, we use as_Spatial() from sf package.
Code
childcare <- as_Spatial(childcare_sf)
mpsz <- as_Spatial(mpsz_sf)
sg <- as_Spatial(sg_sf)To look into the information of the three new Spatial* classes,
Code
childcareclass : SpatialPointsDataFrame
features : 1925
extent : 11810.03, 45404.24, 25596.33, 49300.88 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 2
names : Name, Description
min values : kml_1, <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>100044</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>44, TELOK BLANGAH DRIVE, #01 - 19/51, SINGAPORE 100044</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td>Child Care Services</td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td></td> </tr><tr bgcolor=""> <th>NAME</th> <td>PCF SPARKLETOTS PRESCHOOL @ TELOK BLANGAH BLK 44 (CC)</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>349C54F201805938</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20211201093837</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center>
max values : kml_999, <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>99982</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>35, ALLANBROOKE ROAD, SINGAPORE 099982</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td>Child Care Services</td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td></td> </tr><tr bgcolor=""> <th>NAME</th> <td>ISLANDER PRE-SCHOOL PTE LTD</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>4F63ACF93EFABE7F</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20211201093837</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center> Code
mpszclass : SpatialPolygonsDataFrame
features : 323
extent : 2667.538, 56396.44, 15748.72, 50256.33 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 15
names : OBJECTID, SUBZONE_NO, SUBZONE_N, SUBZONE_C, CA_IND, PLN_AREA_N, PLN_AREA_C, REGION_N, REGION_C, INC_CRC, FMEL_UPD_D, X_ADDR, Y_ADDR, SHAPE_Leng, SHAPE_Area
min values : 1, 1, ADMIRALTY, AMSZ01, N, ANG MO KIO, AM, CENTRAL REGION, CR, 00F5E30B5C9B7AD8, 16409, 5092.8949, 19579.069, 871.554887798, 39437.9352703
max values : 323, 17, YUNNAN, YSSZ09, Y, YISHUN, YS, WEST REGION, WR, FFCCF172717C2EAF, 16409, 50424.7923, 49552.7904, 68083.9364708, 69748298.792 Code
sgclass : SpatialPolygons
features : 1
extent : 2667.538, 56396.44, 15748.72, 50256.33 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 1.5.2. Converting the Spatial* class into generic sp format
spatstat requires the analytical data in to be in ppp object form. As there is no direct way to convert a Spatial* classes into ppp object, we would need to convert the Spatial* classes into Spatial object first.
Code
childcare_sp <- as(childcare, "SpatialPoints")
sg_sp <- as(sg, "SpatialPolygons")Then, we should look into the sp objects properties:
Code
childcare_spclass : SpatialPoints
features : 1925
extent : 11810.03, 45404.24, 25596.33, 49300.88 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs Code
sg_spclass : SpatialPolygons
features : 1
extent : 2667.538, 56396.44, 15748.72, 50256.33 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs With the conversion from Spatial* class into generic sp format, the spatial data frames are converted into spatial objects.
1.5.3 Converting the generic sp format into spatstat’s ppp format
Next, we will use as.ppp() from spatstat package to convert the spatial data into spatstat’s ppp object format:
Code
childcare_ppp <- as(childcare_sp, "ppp")
childcare_pppPlanar point pattern: 1925 points
window: rectangle = [11810.03, 45404.24] x [25596.33, 49300.88] unitsHere, we can plot childcare_ppp to examine the difference.
Code
plot(childcare_ppp)
To have a quick understanding of the summary statistics of the newly created ppp object, we can use the following code:
Code
summary(childcare_ppp)Planar point pattern: 1925 points
Average intensity 2.417323e-06 points per square unit
*Pattern contains duplicated points*
Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units
Window: rectangle = [11810.03, 45404.24] x [25596.33, 49300.88] units
(33590 x 23700 units)
Window area = 796335000 square unitsFrom the above summary, we notice the warning message about duplicates. In spatial point patterns analysis, the presence of duplicates is a significant issue The statistical methodology used for spatial point patterns processes is based largely on the assumption that process are simple, that is, that the points cannot be coincident.
1.5.4. Handling duplicated points
We can check for duplication in a ppp object by using the following code chunk:
Code
any(duplicated(childcare_ppp))[1] TRUETo find out the number of coincident points, we use the multiplicity() function from spatstat package:
Code
multiplicity(childcare_ppp) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 2 1 1 1 1 2 1 1 1 1 1 1 3 1 1
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1
33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 2
49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1
65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
1 3 1 1 1 2 1 10 1 1 1 1 1 1 1 1
81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112
1 1 1 1 1 1 1 2 1 1 3 1 1 1 2 1
113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128
1 2 2 2 1 1 1 1 1 1 1 1 2 1 1 1
129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144
1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1
145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176
1 1 2 2 2 1 1 1 1 1 2 1 4 1 1 2
177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192
1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1
193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208
3 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1
209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224
1 1 1 1 1 10 1 1 3 1 1 1 1 1 1 1
225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240
1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256
1 1 2 6 1 2 1 1 2 1 1 1 1 1 1 1
257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272
3 2 3 2 1 2 1 1 2 4 1 6 6 1 1 1
273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288
2 1 1 1 1 2 1 1 1 1 1 1 3 1 1 1
289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304
1 1 4 1 2 1 1 1 1 1 1 1 1 1 1 1
305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320
1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352
1 1 2 1 1 1 2 1 1 1 2 1 1 1 1 1
353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368
1 1 1 1 2 1 2 2 1 1 1 1 2 1 1 1
369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384
4 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1
385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416
2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4
417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448
1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1
449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464
1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1
465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480
1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1
481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496
2 2 1 1 1 1 1 10 1 2 1 1 1 2 1 3
497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512
1 1 1 1 10 10 10 1 1 1 1 1 1 1 1 1
513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528
1 1 1 2 1 2 1 1 1 1 3 1 2 1 1 1
529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544
1 1 1 1 1 1 3 1 1 1 1 1 2 1 1 2
545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560
1 1 3 1 1 1 1 1 1 1 1 2 2 2 1 1
561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576
2 3 1 1 1 2 1 1 1 2 2 1 1 1 1 1
577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592
1 1 1 1 1 1 1 1 1 1 1 1 1 4 1 1
593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608
1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1
609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624
1 1 1 1 1 4 1 1 1 1 1 1 4 1 1 1
625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640
1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656
1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1
657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672
1 1 1 1 1 1 1 1 1 1 2 1 1 3 1 1
673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688
1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 2
689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720
1 1 1 2 1 2 1 10 1 4 1 2 1 1 1 1
721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736
3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768
1 3 1 1 3 1 1 1 1 2 1 1 1 1 1 1
769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800
1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896
1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2
897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912
1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928
1 1 2 1 1 1 1 1 2 2 1 1 1 1 2 1
929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944
1 1 2 1 2 1 1 1 2 1 1 1 2 1 1 1
945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960
1 1 2 1 1 2 1 1 1 1 1 1 1 1 2 1
961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976
1 2 2 1 1 1 1 2 1 1 1 1 2 1 1 2
977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992
1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024
1 1 1 2 4 1 1 1 1 1 1 2 1 2 2 2
1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040
2 1 1 1 1 2 1 1 2 2 2 2 1 1 1 1
1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056
2 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1
1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072
1 2 2 2 1 1 1 1 1 2 1 1 2 2 2 1
1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088
1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1
1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104
1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120
2 1 2 1 2 1 1 1 1 1 1 2 2 1 1 2
1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136
1 2 1 2 1 2 1 1 1 1 1 2 1 1 1 1
1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152
1 2 1 2 2 2 2 2 1 1 1 1 1 2 1 1
1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168
1 1 1 1 1 2 1 1 2 1 1 1 1 2 1 1
1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184
1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1
1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200
1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1
1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232
1 1 1 2 1 1 1 3 1 1 1 1 1 1 1 10
1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248
2 1 3 2 1 2 1 1 2 3 2 1 1 1 1 1
1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264
1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1
1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280
1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1
1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296
2 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1
1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328
10 1 2 4 1 1 1 4 1 4 1 1 1 1 1 1
1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344
1 1 1 1 1 1 1 1 1 4 2 3 2 1 1 1
1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360
2 2 1 1 1 1 1 2 2 3 1 1 1 1 1 2
1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392
2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424
1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440
2 2 2 1 1 1 6 1 1 1 1 1 1 1 1 1
1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456
1 1 1 4 1 1 1 1 1 1 1 1 1 1 1 1
1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472
1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1
1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488
1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1
1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504
2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520
2 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1
1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552
1 1 1 1 1 1 1 1 1 6 1 1 1 1 1 1
1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568
1 1 1 1 1 1 1 3 1 1 4 1 1 2 1 1
1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584
2 1 1 1 2 1 4 1 2 1 1 1 1 1 1 1
1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600
1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1
1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616
1 1 1 1 2 1 1 3 1 1 1 2 1 1 1 1
1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632
2 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1
1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648
3 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1
1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664
1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1
1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680
1 1 1 4 1 1 1 6 1 1 1 1 1 1 1 1
1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696
1 1 1 2 1 1 1 2 1 1 1 1 1 2 1 1
1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712
1 2 1 1 1 1 1 1 1 1 2 2 2 1 1 1
1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728
2 1 2 1 2 1 2 1 1 2 1 2 2 2 2 1
1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744
1 1 1 1 1 2 1 1 1 2 1 1 1 1 2 1
1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760
1 4 1 4 1 4 1 1 2 1 1 1 1 1 3 1
1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776
1 1 1 2 2 2 2 2 2 2 2 1 1 2 2 2
1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792
1 2 1 1 1 1 1 2 2 2 1 2 2 2 2 1
1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808
2 1 1 1 1 1 1 1 2 2 1 2 1 1 1 1
1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824
1 1 1 1 2 1 2 2 2 2 2 2 1 1 2 1
1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840
1 1 1 2 2 2 2 2 1 1 1 2 1 1 2 2
1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856
1 2 1 1 2 1 1 2 2 2 1 2 1 2 1 1
1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872
1 1 1 1 1 1 2 1 1 1 1 4 1 1 1 1
1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888
3 1 1 2 1 1 1 2 1 1 1 1 1 2 2 1
1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904
1 1 2 1 2 2 1 1 1 1 1 2 1 1 2 1
1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920
1 3 2 2 2 1 2 1 3 1 1 1 1 1 1 1
1921 1922 1923 1924 1925
1 1 1 1 3 To find out how many locations have more than one point event, we can use the code:
Code
sum(multiplicity(childcare_ppp) > 1)[1] 338The output shows that there are 338 duplicated point events.
To view the location of these duplicate point events, we will plot childcare data with the following code chunk:
Code
tmap_mode('view')
tm_shape(childcare) +
tm_dots(alpha=0.4,
size = 0.05)From the graph above, we can spot the duplicate point events as the duplicate points overlap, resulting in darker points in the map.
After plotting the graph, we adjust our tmap_mode back to static setting:
Code
tmap_mode('plot')To overcome the issue of duplicate points, we can use any of the following 3 solutions:
Delete the duplicates (however, this would lead to the loss of some useful point events)
Jittering: To add a small pertubation to the duplicate points, so that they do not occupy the exact same space
Make each point “unique”, and attach the duplicates of the points to the patterns as marks, as attributes of the points. Then, we would need analytical techniques that take into account these marks.
Code
childcare_ppp_jit <- rjitter(childcare_ppp,
retry=TRUE,
nsim = 1,
drop = TRUE)Code
any(duplicated(childcare_ppp_jit))[1] FALSE1.5.5 Creating owin object
When analysing spatial point patterns, it is a good practice to confine the analysis within a geographical area like Singapore’s boundary. In spatstat, an object called owin is designed to represent this polygonal region.
The code chunk below is used to convert sg sf object into owin object of spatstat.
Code
sg_owin <- as.owin(sg_sf)The output object can be displayed by using the plot() function
Code
plot(sg_owin)
and summary() function of Base R.
Code
summary(sg_owin)Window: polygonal boundary
80 separate polygons (35 holes)
vertices area relative.area
polygon 1 14650 6.97996e+08 8.93e-01
polygon 2 (hole) 3 -2.21090e+00 -2.83e-09
polygon 3 285 1.61128e+06 2.06e-03
polygon 4 (hole) 3 -2.05920e-03 -2.63e-12
polygon 5 (hole) 3 -8.83647e-03 -1.13e-11
polygon 6 668 5.40368e+07 6.91e-02
polygon 7 44 2.26577e+03 2.90e-06
polygon 8 27 1.50315e+04 1.92e-05
polygon 9 711 1.28815e+07 1.65e-02
polygon 10 (hole) 36 -4.01660e+04 -5.14e-05
polygon 11 (hole) 317 -5.11280e+04 -6.54e-05
polygon 12 (hole) 3 -3.41405e-01 -4.37e-10
polygon 13 (hole) 3 -2.89050e-05 -3.70e-14
polygon 14 77 3.29939e+05 4.22e-04
polygon 15 30 2.80002e+04 3.58e-05
polygon 16 (hole) 3 -2.83151e-01 -3.62e-10
polygon 17 71 8.18750e+03 1.05e-05
polygon 18 (hole) 3 -1.68316e-04 -2.15e-13
polygon 19 (hole) 36 -7.79904e+03 -9.97e-06
polygon 20 (hole) 4 -2.05611e-02 -2.63e-11
polygon 21 (hole) 3 -2.18000e-06 -2.79e-15
polygon 22 (hole) 3 -3.65501e-03 -4.67e-12
polygon 23 (hole) 3 -4.95057e-02 -6.33e-11
polygon 24 (hole) 3 -3.99521e-02 -5.11e-11
polygon 25 (hole) 3 -6.62377e-01 -8.47e-10
polygon 26 (hole) 3 -2.09065e-03 -2.67e-12
polygon 27 91 1.49663e+04 1.91e-05
polygon 28 (hole) 26 -1.25665e+03 -1.61e-06
polygon 29 (hole) 349 -1.21433e+03 -1.55e-06
polygon 30 (hole) 20 -4.39069e+00 -5.62e-09
polygon 31 (hole) 48 -1.38338e+02 -1.77e-07
polygon 32 (hole) 28 -1.99862e+01 -2.56e-08
polygon 33 40 1.38607e+04 1.77e-05
polygon 34 (hole) 40 -6.00381e+03 -7.68e-06
polygon 35 (hole) 7 -1.40545e-01 -1.80e-10
polygon 36 (hole) 12 -8.36709e+01 -1.07e-07
polygon 37 45 2.51218e+03 3.21e-06
polygon 38 142 3.22293e+03 4.12e-06
polygon 39 148 3.10395e+03 3.97e-06
polygon 40 75 1.73526e+04 2.22e-05
polygon 41 83 5.28920e+03 6.76e-06
polygon 42 211 4.70521e+05 6.02e-04
polygon 43 106 3.04104e+03 3.89e-06
polygon 44 266 1.50631e+06 1.93e-03
polygon 45 71 5.63061e+03 7.20e-06
polygon 46 10 1.99717e+02 2.55e-07
polygon 47 478 2.06120e+06 2.64e-03
polygon 48 155 2.67502e+05 3.42e-04
polygon 49 1027 1.27782e+06 1.63e-03
polygon 50 (hole) 3 -1.16959e-03 -1.50e-12
polygon 51 65 8.42861e+04 1.08e-04
polygon 52 47 3.82087e+04 4.89e-05
polygon 53 6 4.50259e+02 5.76e-07
polygon 54 132 9.53357e+04 1.22e-04
polygon 55 (hole) 3 -3.23310e-04 -4.13e-13
polygon 56 4 2.69313e+02 3.44e-07
polygon 57 (hole) 3 -1.46474e-03 -1.87e-12
polygon 58 1045 4.44510e+06 5.68e-03
polygon 59 22 6.74651e+03 8.63e-06
polygon 60 64 3.43149e+04 4.39e-05
polygon 61 (hole) 3 -1.98390e-03 -2.54e-12
polygon 62 (hole) 4 -1.13774e-02 -1.46e-11
polygon 63 14 5.86546e+03 7.50e-06
polygon 64 95 5.96187e+04 7.62e-05
polygon 65 (hole) 4 -1.86410e-02 -2.38e-11
polygon 66 (hole) 3 -5.12482e-03 -6.55e-12
polygon 67 (hole) 3 -1.96410e-03 -2.51e-12
polygon 68 (hole) 3 -5.55856e-03 -7.11e-12
polygon 69 234 2.08755e+06 2.67e-03
polygon 70 10 4.90942e+02 6.28e-07
polygon 71 234 4.72886e+05 6.05e-04
polygon 72 (hole) 13 -3.91907e+02 -5.01e-07
polygon 73 15 4.03300e+04 5.16e-05
polygon 74 227 1.10308e+06 1.41e-03
polygon 75 10 6.60195e+03 8.44e-06
polygon 76 19 3.09221e+04 3.95e-05
polygon 77 145 9.61782e+05 1.23e-03
polygon 78 30 4.28933e+03 5.49e-06
polygon 79 37 1.29481e+04 1.66e-05
polygon 80 4 9.47108e+01 1.21e-07
enclosing rectangle: [2667.54, 56396.44] x [15748.72, 50256.33] units
(53730 x 34510 units)
Window area = 781945000 square units
Fraction of frame area: 0.4221.5.6 Combining point events object and owin object
In this last step of geospatial data wrangling, we will extract childcare events that are located within Singapore by using the code chunk below.
Code
childcareSG_ppp <- childcare_ppp[sg_owin]The output object combined both the point and polygon feature in one ppp object class as shown below.
Code
summary(childcareSG_ppp)Planar point pattern: 1925 points
Average intensity 2.461811e-06 points per square unit
*Pattern contains duplicated points*
Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units
Window: polygonal boundary
80 separate polygons (35 holes)
vertices area relative.area
polygon 1 14650 6.97996e+08 8.93e-01
polygon 2 (hole) 3 -2.21090e+00 -2.83e-09
polygon 3 285 1.61128e+06 2.06e-03
polygon 4 (hole) 3 -2.05920e-03 -2.63e-12
polygon 5 (hole) 3 -8.83647e-03 -1.13e-11
polygon 6 668 5.40368e+07 6.91e-02
polygon 7 44 2.26577e+03 2.90e-06
polygon 8 27 1.50315e+04 1.92e-05
polygon 9 711 1.28815e+07 1.65e-02
polygon 10 (hole) 36 -4.01660e+04 -5.14e-05
polygon 11 (hole) 317 -5.11280e+04 -6.54e-05
polygon 12 (hole) 3 -3.41405e-01 -4.37e-10
polygon 13 (hole) 3 -2.89050e-05 -3.70e-14
polygon 14 77 3.29939e+05 4.22e-04
polygon 15 30 2.80002e+04 3.58e-05
polygon 16 (hole) 3 -2.83151e-01 -3.62e-10
polygon 17 71 8.18750e+03 1.05e-05
polygon 18 (hole) 3 -1.68316e-04 -2.15e-13
polygon 19 (hole) 36 -7.79904e+03 -9.97e-06
polygon 20 (hole) 4 -2.05611e-02 -2.63e-11
polygon 21 (hole) 3 -2.18000e-06 -2.79e-15
polygon 22 (hole) 3 -3.65501e-03 -4.67e-12
polygon 23 (hole) 3 -4.95057e-02 -6.33e-11
polygon 24 (hole) 3 -3.99521e-02 -5.11e-11
polygon 25 (hole) 3 -6.62377e-01 -8.47e-10
polygon 26 (hole) 3 -2.09065e-03 -2.67e-12
polygon 27 91 1.49663e+04 1.91e-05
polygon 28 (hole) 26 -1.25665e+03 -1.61e-06
polygon 29 (hole) 349 -1.21433e+03 -1.55e-06
polygon 30 (hole) 20 -4.39069e+00 -5.62e-09
polygon 31 (hole) 48 -1.38338e+02 -1.77e-07
polygon 32 (hole) 28 -1.99862e+01 -2.56e-08
polygon 33 40 1.38607e+04 1.77e-05
polygon 34 (hole) 40 -6.00381e+03 -7.68e-06
polygon 35 (hole) 7 -1.40545e-01 -1.80e-10
polygon 36 (hole) 12 -8.36709e+01 -1.07e-07
polygon 37 45 2.51218e+03 3.21e-06
polygon 38 142 3.22293e+03 4.12e-06
polygon 39 148 3.10395e+03 3.97e-06
polygon 40 75 1.73526e+04 2.22e-05
polygon 41 83 5.28920e+03 6.76e-06
polygon 42 211 4.70521e+05 6.02e-04
polygon 43 106 3.04104e+03 3.89e-06
polygon 44 266 1.50631e+06 1.93e-03
polygon 45 71 5.63061e+03 7.20e-06
polygon 46 10 1.99717e+02 2.55e-07
polygon 47 478 2.06120e+06 2.64e-03
polygon 48 155 2.67502e+05 3.42e-04
polygon 49 1027 1.27782e+06 1.63e-03
polygon 50 (hole) 3 -1.16959e-03 -1.50e-12
polygon 51 65 8.42861e+04 1.08e-04
polygon 52 47 3.82087e+04 4.89e-05
polygon 53 6 4.50259e+02 5.76e-07
polygon 54 132 9.53357e+04 1.22e-04
polygon 55 (hole) 3 -3.23310e-04 -4.13e-13
polygon 56 4 2.69313e+02 3.44e-07
polygon 57 (hole) 3 -1.46474e-03 -1.87e-12
polygon 58 1045 4.44510e+06 5.68e-03
polygon 59 22 6.74651e+03 8.63e-06
polygon 60 64 3.43149e+04 4.39e-05
polygon 61 (hole) 3 -1.98390e-03 -2.54e-12
polygon 62 (hole) 4 -1.13774e-02 -1.46e-11
polygon 63 14 5.86546e+03 7.50e-06
polygon 64 95 5.96187e+04 7.62e-05
polygon 65 (hole) 4 -1.86410e-02 -2.38e-11
polygon 66 (hole) 3 -5.12482e-03 -6.55e-12
polygon 67 (hole) 3 -1.96410e-03 -2.51e-12
polygon 68 (hole) 3 -5.55856e-03 -7.11e-12
polygon 69 234 2.08755e+06 2.67e-03
polygon 70 10 4.90942e+02 6.28e-07
polygon 71 234 4.72886e+05 6.05e-04
polygon 72 (hole) 13 -3.91907e+02 -5.01e-07
polygon 73 15 4.03300e+04 5.16e-05
polygon 74 227 1.10308e+06 1.41e-03
polygon 75 10 6.60195e+03 8.44e-06
polygon 76 19 3.09221e+04 3.95e-05
polygon 77 145 9.61782e+05 1.23e-03
polygon 78 30 4.28933e+03 5.49e-06
polygon 79 37 1.29481e+04 1.66e-05
polygon 80 4 9.47108e+01 1.21e-07
enclosing rectangle: [2667.54, 56396.44] x [15748.72, 50256.33] units
(53730 x 34510 units)
Window area = 781945000 square units
Fraction of frame area: 0.422To plot the newly derived childcareSG_ppp map,
Code
plot(childcareSG_ppp)
1.6 First-Order Spatial Point Patterns Analysis
In this section, we will learn how to perform first-order SPPA by using spatstat package. The hands-on exercise will focus on:
deriving kernel density estimation (KDE) layer for visualising and exploring the intensity of point processes, and
performing Confirmatory Spatial Point Patterns Analysis by using Nearest Neighbour statistics.
1.6.1 Kernel Density Estimation (KDE)
In this section, we will learn how to compute the kernel density estimation (KDE) of childcare services in Singapore.
1.6.1.1 Computing KDE using automatic bandwidth selection method
The code chunk below computes a Kernel Density by using the following configurations of density() of spatstat:
Automatic bandwidth selection method: bw.diggle()
- Other recommended methods: bw.CvL(), bw.scott() or bw.ppl()
Smoothing kernel: “gaussian”
- Other smoothing methods: “epanechnikov”, “quartic” or “disc”
The intensity estimate is corrected for edge effect bias by using method described by Jones (1993) and Diggle (2010, equation 18.9). The default is FALSE.
Code
kde_childcareSG_bw <- density(childcareSG_ppp,
sigma = bw.diggle,
edge = TRUE,
kernel = "gaussian")The plot() function of Base R is then used to display the kernel density derived.
Code
plot(kde_childcareSG_bw)
The density values of the output range from 0 to 0.00003 which is way too small to comprehend. This is because the default unit of measurement of svy21 is in meter. As a result, the density values computed is in “number of points per square meter”.
Before we move on to next section, it is good to know that you can retrieve the bandwidth used to compute the kde layer by using the code chunk below.
Code
bw <- bw.diggle(childcareSG_ppp)
bw sigma
295.4419 1.6.1.2 Rescaling KDE values
In the following code chunk, rescale() is used to convert the unit of measurement from meter to kilometer.
Code
childcareSG_ppp.km <- rescale (childcareSG_ppp, 1000, "km")Now, we can re-run density() using the rescaled data set and plot the output kde map.
Code
kde_childcareSG.bw.km <- density(childcareSG_ppp.km,
sigma = bw.diggle,
edge = TRUE,
kernel = "gaussian")
plot(kde_childcareSG.bw.km)
Now, we can see that the output image looks identical to the earlier version, but with more intepretable data values in the legend.
1.6.1.3 Working with different automatic bandwidth methods
Beside bw.diggle(), I mentioned that there are three other spatstat functions that can be used to determine the bandwidth, which are: bw.CvL(), bw.scott(), and bw.ppl().
Let us take a look at the bandwidth return by these automatic bandwidth calculation methods by using the code chunk below.
Code
bw.CvL(childcareSG_ppp.km) sigma
4.54311 Code
bw.scott(childcareSG_ppp.km) sigma.x sigma.y
2.159749 1.396455 Code
bw.ppl(childcareSG_ppp.km) sigma
0.3897017 Baddeley et. (2016) suggested the use of the bw.ppl() algorithm because based on their experience, it tends to produce more appropriate values when the pattern consists predominantly of tight clusters.
However, they also insist that if the purpose of a study is to detect a single tight cluster in the midst of random noise, the bw.diggle() method seems to work best.
The following code chunk is used to compare the difference in output using bw.diggle and bw.ppl() methods.
Code
kde_childcareSG.ppl <- density(childcareSG_ppp.km,
sigma = bw.ppl,
edge = TRUE,
kernel = "gaussian")
par(mfrow=c(1,2))
plot(kde_childcareSG.bw.km, main = "bw.diggle")
plot(kde_childcareSG.ppl, main = "bw.ppl")
1.6.1.4 Working with different kernel methods
By default, the kernel method used in density.ppp() is Gaussian. However, there are three other options, namely: Epanechnikov, Quartic and Dics.
The code chunk below will be used to compute 3 more kernel density estimations by using these 3 kernel functions.
Code
par(mfrow=c(2,2))
plot(density(childcareSG_ppp.km,
sigma = bw.ppl,
edge = TRUE,
kernel = "gaussian"),
main = "gaussian")
plot(density(childcareSG_ppp.km,
sigma = bw.ppl,
edge = TRUE,
kernel = "epanechnikov"),
main = "Epanechnikov")
plot(density(childcareSG_ppp.km,
sigma = bw.ppl,
edge = TRUE,
kernel = "quartic"),
main = "quartic")
plot(density(childcareSG_ppp.km,
sigma = bw.ppl,
edge = TRUE,
kernel = "disc"),
main = "disc")
1.6.1.5 Fixed and Adaptive KDE
1.6.1.5.1 Computing KDE by using fixed bandwidth
Next, you will compute a KDE layer by defining a bandwidth of 600 meter.
Notice that in the code chunk below, the sigma value used is 0.6. This is because the unit of measurement of childcareSG_ppp.km object is in kilometer, hence the 600m is 0.6km.
Code
kde_childcareSG_600 <- density(childcareSG_ppp.km,
sigma = 0.6,
edge = TRUE,
kernel = "gaussian")
plot (kde_childcareSG_600)
1.6.1.5.2 Computing KDE by using adaptive bandwidth
Fixed bandwidth method is very sensitive to highly skewed distribution of spatial point patterns over geographical units (for example, urban versus rural). One way to overcome this problem is by using adaptive bandwidth instead.
In this section, we will learn how to derive adaptive kernel density estimation by using density.adaptive() of spatstat.
Code
kde_childcareSG_adaptive <- adaptive.density(childcareSG_ppp.km,
method = "kernel")
plot(kde_childcareSG_adaptive)
We can compare the fixed and adaptive kernel density estimation outputs by using the code chunk below:
Code
par(mfrow=c(1,2))
plot(kde_childcareSG.bw.km, main = "Fixed bandwidth")
plot(kde_childcareSG_adaptive, main = "Adaptive bandwidth")
1.6.1.6 Converting KDE output into grid object
The result is the same, but we convert it so that it is suitable for mapping purposes.
Code
gridded_kde_childcareSG_bw <- as.SpatialGridDataFrame.im(kde_childcareSG.bw.km)
spplot(gridded_kde_childcareSG_bw)
1.6.1.7 Converting gridded output into raster
Next, we will convert the gridded kernel density objects into RasterLayer object by using raster() of raster package.
Code
kde_childcareSG_bw_raster <- raster(gridded_kde_childcareSG_bw)Let us take a look at the properties of kde_childcareSG_bw_raster RasterLayer object.
Code
kde_childcareSG_bw_rasterclass : RasterLayer
dimensions : 128, 128, 16384 (nrow, ncol, ncell)
resolution : 0.419757, 0.2695907 (x, y)
extent : 2.667538, 56.39644, 15.74872, 50.25633 (xmin, xmax, ymin, ymax)
crs : NA
source : memory
names : v
values : -1.293897e-14, 37.27443 (min, max)Notice that the crs property is NA.
1.6.1.8 Assigning projection systems
Since the crs property of kde_childcareSG_bw_raster RasterLayer object is NA, we will include CRS information for it using the code below.
Code
projection(kde_childcareSG_bw_raster) <- CRS("+init=EPSG:3414")
kde_childcareSG_bw_rasterclass : RasterLayer
dimensions : 128, 128, 16384 (nrow, ncol, ncell)
resolution : 0.419757, 0.2695907 (x, y)
extent : 2.667538, 56.39644, 15.74872, 50.25633 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +units=m +no_defs
source : memory
names : v
values : -1.293897e-14, 37.27443 (min, max)Now, we see that the crs property is complete.
1.6.1.9 Visualising the output in tmap
Finally, we will display the raster in cartographic quality map using tmap package.
Code
tmap_mode("plot")
tm_shape (kde_childcareSG_bw_raster) +
tm_raster("v") +
tm_layout(legend.position = c("right", "bottom"),
frame = FALSE)
Notice that the raster values are encoded explicitly onto the raster pixel using the values in the “v” field.
1.6.1.10 Comparing Spatial Point Patterns using KDE
In this section, we will learn to compare KDE of childcare at Punggol, Tampines, Choa Chu Kang and Jurong West planning areas.
1.6.1.10.1 Extracting study area
The code chunk below will be used to extract the target planning areas.
Code
pg <- mpsz[mpsz@data$PLN_AREA_N == "PUNGGOL", ]
tm <- mpsz[mpsz@data$PLN_AREA_N == "TAMPINES", ]
ck <- mpsz[mpsz@data$PLN_AREA_N == "CHOA CHU KANG", ]
jw <- mpsz[mpsz@data$PLN_AREA_N == "JURONG WEST", ] Plotting target planning areas:
Code
par(mfrow = c(2,2))
plot(pg, main = "Punggol")
plot(tm, main = "Tampines")
plot(ck, main= "Choa Chu Kang")
plot(jw, main = "Jurong West")
1.6.1.10.2 Converting the spatial point data frame into generic sp format
Next, we will convert these SpatialPolygonsDataFrame layers into generic spatialpolygons layers.
Code
pg_sp <- as(pg,"SpatialPolygons")
tm_sp <- as(tm,"SpatialPolygons")
ck_sp <- as(ck, "SpatialPolygons")
jw_sp <- as(jw,"SpatialPolygons")1.6.1.10.3 Creating owin object
Now, we will convert these SpatialPolygons objects into owin objects that is required by spatstat.
Code
pg_owin <- as(pg_sp, "owin")
tm_owin <- as(tm_sp, "owin")
ck_owin <- as(ck_sp, "owin")
jw_owin <- as(jw_sp, "owin")1.6.1.10.4 Combining childcare points and the study area
By using the code chunk below, we can extract the childcare centres that are within specific regions to conduct out analysis later on.
Code
childcare_pg_ppp <- childcare_ppp_jit[pg_owin]
childcare_tm_ppp <- childcare_ppp_jit[tm_owin]
childcare_ck_ppp <- childcare_ppp_jit[ck_owin]
childcare_jw_ppp <- childcare_ppp_jit[jw_owin]Next, we use rescale() to transform the unit of measurement from metre to kilometre.
Code
childcare_pg_ppp.km <- rescale(childcare_pg_ppp, 1000, "km")
childcare_tm_ppp.km <- rescale(childcare_tm_ppp, 1000, "km")
childcare_ck_ppp.km <- rescale(childcare_ck_ppp, 1000, "km")
childcare_jw_ppp.km <- rescale(childcare_jw_ppp, 1000, "km")The code chunk below is used to plot these four study areas and the location of the childcare centres.
Code
par(mfrow=c(2,2))
plot(childcare_pg_ppp.km, main = "Punggol")
plot(childcare_tm_ppp.km, main = "Tampines")
plot(childcare_ck_ppp.km, main = "Choa Chu Kang")
plot(childcare_jw_ppp.km, main = "Jurong West")
1.6.1.10.5 Computing KDE
The code chunk below will then be used to compute the KDE of these four planning areas. bw.diggle method is used to derive the bandwidth of each.
Code
par(mfrow=c(2,2))
plot(density(childcare_pg_ppp.km,
sigma = bw.diggle,
edge = TRUE,
kernel = "gaussian"),
main = "Punggol")
plot(density(childcare_tm_ppp.km,
sigma = bw.diggle,
edge = TRUE,
kernel = "gaussian"),
main = "Tampines")
plot(density(childcare_ck_ppp.km,
sigma = bw.diggle,
edge = TRUE,
kernel = "gaussian"),
main = "Choa Chu Kang")
plot(density(childcare_jw_ppp.km,
sigma = bw.diggle,
edge = TRUE,
kernel = "gaussian"),
main = "Jurong West")
1.6.1.10.6 Computing fixed bandwidth KDE
For comparison purposes, we will use 250m as the bandwidth.
Code
par(mfrow=c(2,2))
plot(density(childcare_pg_ppp.km,
sigma = 0.25,
edge = TRUE,
kernel = "gaussian"),
main = "Punggol")
plot(density(childcare_tm_ppp.km,
sigma = 0.25,
edge = TRUE,
kernel = "gaussian"),
main = "Tampines")
plot(density(childcare_ck_ppp.km,
sigma = 0.25,
edge = TRUE,
kernel = "gaussian"),
main = "Choa Chu Kang")
plot(density(childcare_jw_ppp.km,
sigma = 0.25,
edge = TRUE,
kernel = "gaussian"),
main = "Jurong West")
1.6.2 Nearest Neighbour Analysis
In this section, we will perform the Clark-Evans test of aggregation for a spatial point pattern by using clarkevans.test() of statspat.
The test hypotheses are:
Ho = The distribution of childcare services are randomly distributed.
H1= The distribution of childcare services are not randomly distributed.
The 95% confident interval will be used.
1.6.2.1 Testing spatial point patterns using Clark and Evans Test
Code
clarkevans.test(childcare_ppp,
correction = "none",
clipregion = "sg_owin",
alternative = c("clustered"),
nsim = 99)
Clark-Evans test
No edge correction
Z-test
data: childcare_ppp
R = 0.49084, p-value < 2.2e-16
alternative hypothesis: clustered (R < 1)Since the p-value < 0.05, we have sufficient evidence at 95% confidence level that the childcare services in Singapore are not randomly distributed.
1.6.2.1.1 Clark and Evans Test: Choa Chu Kang Planning Area
In the code chunk below, clarkevans.test() of spatstat is used to performs Clark-Evans test of aggregation for childcare centre in Choa Chu Kang planning area.
Code
clarkevans.test(childcare_ck_ppp,
correction = "none",
clipregion = NULL,
alternative = c("two.sided"),
nsim = 999)
Clark-Evans test
No edge correction
Z-test
data: childcare_ck_ppp
R = 0.8407, p-value = 0.008751
alternative hypothesis: two-sidedSince the p-value > 0.05, we do not have sufficient evidence at 95% confidence level that the childcare services in Choa Chu Kang are not randomly distributed.
1.6.2.1.2 Clark and Evans Test: Tampines Planning Area
Code
clarkevans.test(childcare_tm_ppp,
correction = "none",
clipregion = NULL,
alternative = c("two.sided"),
nsim = 999)
Clark-Evans test
No edge correction
Z-test
data: childcare_tm_ppp
R = 0.70299, p-value = 7.952e-10
alternative hypothesis: two-sidedSince p-value < 0.05, we have sufficient evidence at 95% confidence level that the childcare services in Tampines are not randomly distributed.
1.7 Second-order Spatial Point Patterns Analysis
1.7.1 Analyzing Spatial Point Process using G-function
The G function measures the distribution of the distances from an arbitrary event to its nearest event.
In this section, we will learn how to compute G-function estimation by using Gest() of spatstat package. We will also learn how to perform Monta Carlo simulation test of Complete Spatial Randomness (CSR) using envelope() of spatstat package.
1.7.1.1 Choa Chu Kang Planning Area
1.7.1.1.1 Computing G-function estimation
The code chunk below is used to compute G-function using Gest() of spatstat package.
Code
G_CK <- Gest(childcare_ck_ppp,
correction = "border")
plot(G_CK, xlim=c(0,500))
1.7.1.1.2 Performing Complete Spatial Randomness (CSR) test
To confirm the observed spatial patterns above, a hypothesis test will be conducted.
The hypothesis and test are as follows:
Ho = The distribution of childcare services at Choa Chu Kang are randomly distributed.
H1= The distribution of childcare services at Choa Chu Kang are not randomly distributed.
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
Monte Carlo test with G-function
Code
G_CK.csr <- envelope(childcare_ck_ppp,
Gest,
nsim = 999)Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.
Done.Code
plot(G_CK.csr)
From the above plot, we can see that the estimated G function lies within the envelope. Hence, it is not statistically significant and we do not have sufficient evidence that the childcare services in Choa Chu Kang are not randomly distributed.
1.7.1.2 Tampines Planning Area
1.7.1.2.1 Computing G-function estimation
Code
G_TM <- Gest(childcare_tm_ppp,
correction = "best")
plot(G_TM)
1.7.1.2.2 Performing Complete Spatial Randomness (CSR) test
To confirm the observed spatial patterns above, a hypothesis test will be conducted.
The hypothesis and test are as follows:
Ho = The distribution of childcare services at Tampines are randomly distributed.
H1= The distribution of childcare services at Tampines are not randomly distributed.
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
Monte Carlo test with G-function
Code
G_TM.csr <- envelope(childcare_tm_ppp, Gest,
correction = "all",
nsim = 999)Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.
Done.Code
plot(G_TM.csr)
From the above plot, we can see that the some parts of the estimated G function lies outside the envelope. Hence, it is statistically significant and we have sufficient evidence that the childcare services in Tampines are not randomly distributed.
1.7.2 Analyzing Spatial Point Process using F-function
The F function estimates the empty space function F(r) or its hazard rate h(r) from a point pattern in a window of arbitrary shape. In this section, we will learn how to compute F-function estimation by using Fest() of spatstat package. We will also learn how to perform Monta Carlo simulation test using envelope() of spatstat package.
1.7.2.1 Choa Chu Kang Planning Area
1.7.2.1.1 Computing F-function estimation
Code
F_CK <- Fest(childcare_ck_ppp)
plot(F_CK)
1.7.2.1.2 Performing Complete Spatial Randomness (CSR) test
To confirm the observed spatial patterns above, a hypothesis test will be conducted.
The hypothesis and test are as follows:
Ho = The distribution of childcare services at Choa Chu Kang are randomly distributed.
H1= The distribution of childcare services at Choa Chu Kang are not randomly distributed.
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
Monte Carlo test with F-function
Code
F_CK.csr <- envelope(childcare_ck_ppp, Fest, nsim = 999)Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.
Done.Code
plot(F_CK.csr)
From the above plot, we can see that the estimated F function lies within the envelope. Hence, it is not statistically significant and we do not have sufficient evidence that the childcare services in Choa Chu Kang are not randomly distributed.
1.7.2.2 Tampines Planning Area
1.7.2.2.1 Computing F-function estimation
Code
F_TM <- Fest(childcare_tm_ppp,
correction = "best")
plot(F_TM)
1.7.2.2.2 Performing Complete Spatial Randomness (CSR) test
To confirm the observed spatial patterns above, a hypothesis test will be conducted.
The hypothesis and test are as follows:
Ho = The distribution of childcare services at Tampines are randomly distributed.
H1= The distribution of childcare services at Tampines are not randomly distributed.
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
Monte Carlo test with F-function
Code
F_TM.csr <- envelope(childcare_tm_ppp, Fest, nsim = 999)Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.
Done.Code
plot(F_TM.csr)
From the above plot, we can see that the some parts of the estimated F function lies outside the envelope. Hence, it is statistically significant and we have sufficient evidence that the childcare services in Tampines are not randomly distributed.
1.7.3 Analying Spatial Point Process using K-function
K-function measures the number of events found up to a given distance of any particular event.
In this section, we will learn how to compute K-function estimates by using Kest() of spatstat package. We will also learn how to perform Monta Carlo simulation test using envelope() of spatstat package.
1.7.3.1 Choa Chu Kang Planning Area
1.7.3.1.1 Computing K-function estimate
Code
K_CK <- Kest(childcare_ck_ppp,
correction = "Ripley")
plot(K_CK, .-r~r, ylab = "K(d) - r", xlab = "d(m)")
1.7.3.1.2 Performing Complete Spatial Randomness (CSR) test
To confirm the observed spatial patterns above, a hypothesis test will be conducted.
The hypothesis and test are as follows:
Ho = The distribution of childcare services at Choa Chu Kang are randomly distributed.
H1= The distribution of childcare services at Choa Chu Kang are not randomly distributed.
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
The code chunk below is used to perform the hypothesis testing.
Code
K_CK.csr <- envelope(childcare_ck_ppp, Kest, nsim = 99, rank =1, glocal = TRUE)Generating 99 simulations of CSR ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,
99.
Done.Code
plot(K_CK.csr, .-r~r, xlab="d", ylab="K(d)-r")
1.7.3.2 Tampines Planning Area
1.7.3.2.1 Computing K-function estimates
Code
K_TM <- Kest(childcare_tm_ppp, correction = "Ripley")
plot(K_TM, . -r~r,
ylab = "K(d) -r",
xlab = "d(m)",
xlim = c(0,1000))
1.7.3.2.2 Performing Complete Spatial Randomness (CSR) test
To confirm the observed spatial patterns above, a hypothesis test will be conducted.
The hypothesis and test are as follows:
Ho = The distribution of childcare services at Tampines are randomly distributed.
H1= The distribution of childcare services at Tampines are not randomly distributed.
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
The code chunk below is used to perform the hypothesis testing.
Code
K_TM.csr <- envelope(childcare_tm_ppp, Kest, nsim = 99, rank = 1, glocal = TRUE)Generating 99 simulations of CSR ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,
99.
Done.Code
plot(K_TM.csr, .-r~r, xlab= "d", ylab = "K(d)-r", xlim = c(0,500))
1.7.4 Analyzing Spatial Point Process using L-function
In this section, we will learn how to compute L-function estimation by using Lest() of spatstat package. We will also learn how to perform Monta Carlo simulation test using envelope() of spatstat package.
1.7.4.1 Choa Chu Kang Planning Area
1.7.4.1.1 Computing L-function estimation
Code
L_CK <- Lest(childcare_ck_ppp, correction = "Ripley")
plot(L_CK, .-r~r,
ylab="L(d)-r", xlab = "d(m)")
1.7.4.1.2 Performing Complete Spatial Randomness (CSR) test
To confirm the observed spatial patterns above, a hypothesis test will be conducted.
The hypothesis and test are as follows:
Ho = The distribution of childcare services at Choa Chu Kang are randomly distributed.
H1= The distribution of childcare services at Choa Chu Kang are not randomly distributed.
The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.
The code chunk below is used to perform the hypothesis testing.
Code
L_CK.csr <- envelope(childcare_ck_ppp, Lest, nsim = 99, rank =1, glocal = TRUE)Generating 99 simulations of CSR ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,
99.
Done.Code
plot(L_CK.csr, .-r~r,
xlab = "d", ylab = "L(d)-r")
1.7.4.2 Tampines Planning Area
1.7.4.2.1 Computing L-function estimate
Code
L_TM <- Lest(childcare_tm_ppp, correction = "Ripley")
plot(L_TM, .-r~r,
ylab = "L(d)-r", xlab = "d(m)",
xlim = c(0,1000))
1.7.4.2.2 Performing Complete Spatial Randomness (CSR) test
To confirm the observed spatial patterns above, a hypothesis test will be conducted.
The hypothesis and test are as follows:
Ho = The distribution of childcare services at Tampines are randomly distributed.
H1= The distribution of childcare services at Tampines are not randomly distributed.
The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.
The code chunk below is used to perform the hypothesis testing.
Code
L_TM.csr <- envelope(childcare_tm_ppp, Lest, nsim = 99, rank = 1, glocal = TRUE)Generating 99 simulations of CSR ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,
99.
Done.Code
plot(L_TM.csr, .-r~r,
xlab = "d", ylab = "L(d)-r", xlim = c(0,500))
2 Network Constrained Spatial Point Patterns Analysis
2.1 Overview
Network Constrained Spatial Point Patterns Analysis (NetSPAA) is a collection of spatial point patterns analysis methods special developed for analysing spatial point events that occur on or along networks. For instance, spatial point events can be locations of traffic accident or childcare centres, and networks can be road networks or river networks.
In this hands-on exercise, we will employ using appropriate functions of spNetwork package:
to derive network constrained kernel density estimation (NetKDE),
and to perform network G-function and k-function analysis
2.2 Data Acquisition
In this study, we will analyse the spatial distribution of childcare centres in Punggol planning area.
For the purpose of this study, two geospatial data sets will be used:
Punggol_St (ESRI shapefile)
- A line features geospatial data which stores the road network within Punggol Planning Area
Punggol_CC (ESRI shapefile)
- A point feature geospatial data which stores the locations of childcare centres within Punggol Planning Area
2.3 Installing and Loading the R Packages
In this exercise, we would be using the following R packages:
sp: provides classes and methods for dealing with spatial data in R. In this exercise, it will be used to manage SpatialPointsDataFrame and SpatiaLinesDataFrame, and for performing projection transformation.
sf: provides simple features access to represent and work with spatial vector data such as points and polygons
spNetwork: provides functions to perform Spatial Point Patterns Analysis such as kernel density estimation (KDE) and K-function on network. It also can be used to build spatial matrices (‘listw’ objects like in ‘spdep’ package) to conduct any kind of traditional spatial analysis with spatial weights based on reticular distances.
tmap provides functions for plotting cartographic quality static point patterns maps or interactive maps by using leaflet API.
classInt: provides a uniform interface to finding class intervals for continuous numerical variables,
viridis: to create colorblind-friendly maps
tidyverse :to provide key data transformation functions
Code
#|eval: FALSE
pacman::p_load(sp, sf, spNetwork, tmap, classInt, viridis, tidyverse)2.4 Data Import and Preparation
To import the geospatial data, we would be using st_read() from the sf package.
Code
#|eval: FALSE
network <- st_read(dsn = "data 1/geospatial",
layer = "Punggol_St")Reading layer `Punggol_St' from data source
`/Users/binhui-ong/IS415-GAA/Hands-on_Ex/Hands-on_Ex03/data 1/geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 2642 features and 2 fields
Geometry type: LINESTRING
Dimension: XY
Bounding box: xmin: 34038.56 ymin: 40941.11 xmax: 38882.85 ymax: 44801.27
Projected CRS: SVY21 / Singapore TMCode
#|eval: FALSE
pg_childcare <- st_read(dsn = "data 1/geospatial",
layer = "Punggol_CC")Reading layer `Punggol_CC' from data source
`/Users/binhui-ong/IS415-GAA/Hands-on_Ex/Hands-on_Ex03/data 1/geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 61 features and 1 field
Geometry type: POINT
Dimension: XYZ
Bounding box: xmin: 34423.98 ymin: 41503.6 xmax: 37619.47 ymax: 44685.77
z_range: zmin: 0 zmax: 0
Projected CRS: SVY21 / Singapore TMWe can examine the contents of the output SpatialLineDataFrame and SpatialPointsDataFrame by using the str() function.
Code
str(network)Classes 'sf' and 'data.frame': 2642 obs. of 3 variables:
$ LINK_ID : num 1.16e+08 1.16e+08 1.16e+08 1.16e+08 1.16e+08 ...
$ ST_NAME : chr "PUNGGOL RD" "PONGGOL TWENTY-FOURTH AVE" "PONGGOL SEVENTEENTH AVE" "PONGGOL SEVENTEENTH AVE" ...
$ geometry:sfc_LINESTRING of length 2642; first list element: 'XY' num [1:2, 1:2] 36547 36559 44575 44614
- attr(*, "sf_column")= chr "geometry"
- attr(*, "agr")= Factor w/ 3 levels "constant","aggregate",..: NA NA
..- attr(*, "names")= chr [1:2] "LINK_ID" "ST_NAME"Code
str(pg_childcare)Classes 'sf' and 'data.frame': 61 obs. of 2 variables:
$ Name : chr "kml_10" "kml_99" "kml_100" "kml_101" ...
$ geometry:sfc_POINT of length 61; first list element: 'XYZ' num 36174 42550 0
- attr(*, "sf_column")= chr "geometry"
- attr(*, "agr")= Factor w/ 3 levels "constant","aggregate",..: NA
..- attr(*, "names")= chr "Name"2.5 Visualising the Geospatial Data
Code
plot(network)
plot(pg_childcare, add = T, col = "red", pch = 19)
Code
tmap_mode('view')
tm_shape(pg_childcare) +
tm_dots() +
tm_shape(network) +
tm_lines()2.6 Network Constrained KDE (NetKDE) Analysis
In this section, we will perform NetKDE analysis by using appropriate functions provided in the spNetwork package.
2.6.1 Preparing the lixels objects
Before computing NetKDE, the SpatialLines object need to be cut into lixels with a specified minimal distance.
This task can be performed by using with lixelize_lines() of spNetwork as shown in the code chunk below.
Code
lixels <- lixelize_lines(network,
700,
mindist = 350)From the code chunk above, we see that:
The length of a lixel, lx_length is set to 700m, and
The minimum length of a lixel, mindist is set to 350m.
Note:
- After cut, if the length of the final lixel is shorter than the minimum distance, then it is added to the previous lixel. If mindist is NULL, then mindist = maxdist/10. The segments that are already shorter than the minimum distance are not modified.
2.6.2 Generating line centre points
Next, lines_center() of spNetwork will be used to generate a SpatialPointsDataFrame (i.e. samples) with line centre points as shown in the code chunk below.
Code
samples <- lines_center(lixels)The points are located at the center of the line based on the length of the line.
2.6.3 Performing NetKDE
Next, we will compute the NetKDE with the code chunk below:
Code
densities <- nkde(network,
events = pg_childcare,
w = rep(1,nrow(pg_childcare)),
samples = samples,
kernel_name = "quartic",
bw = 300,
div = "bw",
method = "simple",
digits = 1,
tol = 1,
grid_shape = c(1,1),
max_depth = 8,
agg = 5,
sparse = TRUE,
verbose = FALSE)From the code chunk above:
kernel_name argument indicates that quartic kernel is used
- Other possible kernel methods supported by spNetwork : triangle, gaussian, scaled gaussian, tricube, cosine ,triweight, epanechnikov or uniform.
method argument indicates that simple method is used to calculate the NKDE.
Currently, spNetwork support three popular methods:
method=“simple”
- An intuitive solution: The distances between events and sampling points are replaced by network distances, and the formula of the kernel is adapted to calculate the density over a linear unit instead of an areal unit.
method=“discontinuous”.
- Equally “divides” the mass density of an event at intersections of lixels.
method=“continuous”
If the “discontinuous” method is unbiased, it leads to a discontinuous kernel function which is a bit counter-intuitive.
This “continuous” method divides the mass of the density at intersection but adjusts the density before the intersection to make the function continuous.
2.6.3.1 Visualising NetKDE
Before we can visualise the NetKDE values, we will use the code chunk below to insert the computed density values (i.e. densities) into samples and lixels objects as a density field.
Code
samples$density <- densities
lixels$density <- densitiesSince the svy21 projection system is in metres, the computed density values are very small i.e. 0.0000005.
Hence, we will rescale the density values from number of events per metre to number of events per kilometre using the code chunk below.
Code
samples$density <- samples$density*1000
lixels$density <- lixels$density*1000Then, we can prepare an interactive and high cartographic quality map visualization using the following code, with appropriate functions of the tmap package.
Code
tmap_mode('view')
tm_shape(lixels) +
tm_lines(col = "density") +
tm_shape(pg_childcare) +
tm_dots()The interactive map above effectively reveals road segments with relatively higher density of childcare centres (darker color) than road segments with relatively lower density of childcare centres (lighter color).
2.7 Network Constrained K- Function Analysis
In this section, we are going to perform the complete spatial randomness (CSR) test by using kfunctions() of spNetwork package. The null hypothesis is defined as:
- Ho: The observed spatial point events (i.e distribution of childcare centres) are uniformly distributed over a street network in Punggol Planning Area.
The CSR test is based on the assumption of the binomial point process which implies the hypothesis that the childcare centres are randomly and independently distributed over the street network.
If this hypothesis is rejected, we may infer that the distribution of childcare centres are spatially interacting and dependent on each other. As a result, they may form nonrandom patterns.
Code
kfun_pg_childcare <- kfunctions(network,
pg_childcare,
start = 0,
end = 1000,
step = 50,
width = 50,
nsim = 50,
resolution = 50,
verbose = FALSE,
conf_int = 0.05)From the code chunk above, we see that there are 10 arguments:
lines: A SpatialLinesDataFrame with the sampling points. The geometries must be a SpatialLinesDataFrame (may crash if some geometries are invalid).
points: A SpatialPointsDataFrame representing the points on the network. These points will be snapped on the network.
start: A double, the start value for evaluating the k and g functions.
end: A double, the last value for evaluating the k and g functions.
step: A double, the jump between two evaluations of the k and g function.
width: The width of each donut for the g-function.
nsim: An integer indicating the number of Monte Carlo simulations required. In the above example, 50 simulation was performed. Note: most of the time, more simulations are required for inference
resolution: When simulating random points on the network, selecting a resolution will reduce greatly the calculation time. When resolution is null the random points can occur everywhere on the graph. If a value is specified, the edges are split according to this value and the random points are selected vertices on the new network.
conf_int: A double indicating the width confidence interval (default = 0.05).
The output of kfunctions() is a list with the following values:
plotkA: a ggplot2 object representing the values of the k-function
plotgA: a ggplot2 object representing the values of the g-function
valuesA: a DataFrame with the values used to build the plots
For instance, we can visualize the ggplot2 object of k-function by using the following code:
Code
kfun_pg_childcare$plotk
The blue line is the empirical network K-function of the childcare centres in Punggol planning area. The grey envelope represents the results of the 50 simulations in the interval 2.5% - 97.5%.
Because the blue line between the distance of 250m-400m are below the grey area, we can infer that the childcare centres in Punggol planning area resemble regular pattern at the distance of 250m-400m.